arXiv subjects

Fernando A Morales

Publications and source records attributed to Fernando A Morales.

13 recordsLinked to original sources

arXiv2022

Expected Performance and Worst Case Scenario Analysis of the Divide-and-Conquer Method for the 0-1 Knapsack Problem

In this paper we furnish quality certificates for the Divide-and-Conquer method solving the 0-1 Knapsack Problem: the worst case scenario and estimates for the expected performance. The probabilistic setting is given and the main random variables are defined for the analysis of the expected performance. The efficiency is rigorously approximated for one iteration of the method then, these values are used to derive analytic estimates for the performance of a general Divide-and-Conquer tree. All the theoretical results are verified with statistically suited numerical experiments for a wider illustration of the method.

cs.DS↗

arXiv2022

Application and Assessment of Divide-and-Conquer-based Heuristic Algorithms for some Integer Optimization Problems

In this paper three heuristic algorithms using the Divide-and-Conquer paradigm are developed and assessed for three integer optimizations problems: Multidimensional Knapsack Problem (d-KP), Bin Packing Problem (BPP) and Travelling Salesman Problem (TSP). For each case, the algorithm is introduced, together with the design of numerical experiments, in order to empirically establish its performance from both points of view: its computational time and its numerical accuracy.

math.OC↗

arXiv2020

A big data based method for pass rates optimization in mathematics university lower division courses

In this paper an algorithm designed for large databases is introduced for the enhancement of pass rates in mathematical university lower division courses with several sections. Using integer programming techniques, the algorithm finds the optimal pairing of students and lecturers in order to maximize the success chances of the students' body. The students-lecturer success probability is computed according to their corresponding profiles stored in the data bases.

econ.GN↗

arXiv2020

Analysis of Divide & Conquer strategies for the 0-1 Minimization Knapsack Problem

We introduce and asses several Divide \& Conquer heuristic strategies aimed to solve large instances of the 0-1 Minimization Knapsack Problem. The method subdivides a large problem in two smaller ones (or recursive iterations of the same principle), to lower down the global computational complexity of the original problem, at the expense of a moderate loss of quality in the solution. Theoretical mathematical results are presented in order to guarantee an algorithmically successful application of the method and to suggest the potential strategies for its implementation. In contrast, due to the lack of theoretical results, the solution's quality deterioration is measured empirically by means of Monte Carlo simulations for several types and values of the chosen strategies. Finally, introducing parameters of efficiency we suggest the best strategies depending on the data input.

cs.DM↗

arXiv2019

The asymptotic analysis of a Darcy-Stokes system coupled through a curved interface

The asymptotic analysis of a Darcy-Stokes system modeling the fluid exchange between a narrow channel (Stokes) and a porous medium (Darcy) coupled through a $ C^{2} $ curved interface, is presented. The channel is a cylindrical domain between the interface ($ Γ$) and a parallel translation of it ($ Γ+ ε\, \boldsymbol{\widehat{e}}_{N} $). The introduction of a change variable to fix the domain's geometry and the introduction of two systems of coordinates: the Cartesian and a local one (consistent with the geometry of the surface), permit to find a Darcy-Brinkman lower dimensional coupled system as the limiting form, when the width of the channel tends to zero ($ ε\rightarrow 0 $).

math.AP↗

arXiv2018

A Discussion on the Transmission Conditions for Saturated Fluid Flow Through Porous Media With Fractal Microstructure

The present work is aimed to find suitable exchange conditions for saturated fluid flow in a porous medium, when a fractal microstructure is embedded in the porous matrix. Two different deterministic models are introduced and rigorously analyzed. Also, numerical experiments for each of them are presented to verify the theoretically predicted behavior of the phenomenon and some probabilistic versions are explored numerically, to gain further insight on the phenomenon.

math.AP↗

arXiv2018

A Conforming Primal-Dual Mixed Formulation for the 2D Multiscale Porous Media Flow Problem

In this paper a new primal-dual mixed finite element method is introduced, aimed to model multiscale problems with several geometric subregions in the domain of interest. In each of these regions porous media fluid flow takes place, but governed by physical parameters at a different scale; additionally, a fluid exchange through contact interfaces occurs between neighboring regions. The well-posedness of the primal-dual mixed finite element formulation on bounded simply connected polygonal domains of the plane is presented. Next, the convergence of the discrete solution to the exact solution of the problem is discussed, together with the convergence rate analysis. Finally, the numerical examples illustrate the method's capabilities to handle multiscale problems and interface discontinuities as well as experimental rates of convergence.

math.NA↗

arXiv2018

Tangential Fluid flow within 3D narrow fissures: Conservative velocity fields on associated triangulations and transport processes

For a fissured medium with uncertainty in the knowledge of fractures' geometry, a conservative tangential flow field is constructed, which is consistent with the physics of stationary fluid flow in porous media and an interpolated geometry of the cracks. The flow field permits computing preferential fluid flow directions of the medium, rates of mechanical energy dissipations and a stochastic matrix modeling stream lines and fluid mass transportation, for the analysis of solute/contaminant mass advection-diffusion as well as drainage times.

math.NA↗

arXiv2016

A Darcy-Brinkman Model of Fractures in Porous Media

For a fully-coupled Darcy-Stokes system describing the exchange of fluid and stress balance across the interface between a saturated porous medium and an open very narrow channel, the limiting problem is characterized as the width of the channel converges to zero. It is proven that the limit problem is a fully-coupled system of Darcy flow in the porous medium with Brinkman flow in tangential coordinates of the lower dimensional interface.

math.AP↗

arXiv2016

The Interaction Between PDE and Graphs in Multiscale Modeling

In this article an upscaled model is presented, for complex networks with highly clustered regions exchanging some abstract quantities in both, microscale and macroscale level. Such an intricate system is approximated by a partitioned open map in $\mathbb{R}^{2}$ or $\mathbb{R}^{3}$. The behavior of the quantities is modeled as flowing in the map constructed and thus it is subject to be described by partial differential equations. We follow this approach using the Darcy Porous Media, saturated fluid flow model in mixed variational formulation.

math.AP↗

arXiv2014

Notes on the nonlinear dependence of a multiscale coupled system with respect to the interface

This work studies the dependence of the solution with respect to interface geometric perturbations in a multiscaled coupled Darcy flow system in direct variational formulation. A set of admissible perturbation functions and a sense of convergence are presented, as well as sufficient conditions on the forcing terms, in order to conclude strong convergence statements. For the rate of convergence of the solutions we start solving completely the one dimensional case using orthogonal decompositions on appropriate subspaces. Finally, the rate of convergence question is analyzed in a simple multiple dimensional setting, studying the nonlinear operators introduced by the geometric perturbations.

math.AP↗

arXiv2014

On the Construction of Geometric Parameters for Preferential Fluid Flow Information in Fissured Media

For a fissured medium, we analyze the impact that the geometry of the cracks, has in the phenomenon of preferential fluid flow. Using finite volume meshes we analyze the mechanical energy dissipation due to gravity, curvature of the surface and friction against its walls. We construct parameters depending on the \emph{Geometry} of the surface which are not valid for direct quantitative purposes, but are reliable for relative comparison of mechanical energy dissipation. Such analysis yields \emph{Information} about the preferential flow directions of the medium which, in most of the cases is not deterministic, therefore the respective \emph{Probability Spaces} are introduced. Finally, we present the concept of \emph{Entropy} linked to the geometry of the surface. This notion follows naturally from the random nature of the \emph{Preferential Flow Information.

math.PR↗

arXiv2013

On the generation of bipartite grids with controlled regularity for 2-D and 3-D simply connected domains

We present a procedure to generate bipartite grids for simply connected domains in 2-D and 3-D of prescribed size and controlled regularity elements. The mesh elements $K$ of the triangulation satisfy $ζ_{K} \leq C$ where $ζ_{K}$ is the regularity and $C$ is a constant depending on the shape parameters of the initial mesh. Bipartite grids permit a well-posed mixed-mixed variational formulation of problems such as the porous media flow equation and other linear physical phenomena as well as Galerkin-type discontinuous relaxations.

math.NA↗